Question

Evaluate 2 tan square 45 degree+cos square 30 degree_sin square 30 degree

Answer 1

Question :-

Evaluate it,

$2 { \tan }^{2} 45 \degree + { \cos }^{2} 30 \degree - { \sin}^{2} 30 \degree \:$

Answer:-

$\implies \: \frac{5}{2}$

Used Values :-

• tan 45° = 1
• cos 30° = √3/2
• sin 30° = 1/2

Solution :-

$\implies \: 2 { \tan }^{2} 45 \degree + { \cos }^{2} 30 \degree - { \sin}^{2} 30 \degree \: \: \\ \\ \bold{\mathfrak{substitute \: the \: given \: values \: }} \\ \\ \implies \: 2 \times {(1)}^{2} + { \bigg( \frac{ \sqrt{3} }{2} \bigg) }^{2} - { \bigg(\frac{1}{2} \bigg)}^{2} \\ \\ \implies \: 2 + \frac{3}{4} - \frac{1}{4} \\ \\ \implies \: \frac{8 + 3 - 1}{4} \\ \\ \implies \: \frac{10}{4} \\ \\ \implies \: \frac{5}{2}$

Hope it helps you.